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On time-harmonic Maxwell equations with nonhomogeneous conductivities: Solvability and FE-approximation. (English) Zbl 0696.65085
The authors analyze the solvability of the 3D problem: \(rot H=E\) in \(\Omega,\) \(rot E=-i^{\omega \mu}H\) in \(\Omega\) and \(nx E=nx \tilde E\) on \(\partial\Omega,\) where E, H are complex-valued vector functions independent of time, \(\epsilon\) is the electric dielectricity, \(\mu\) the magnetic permeability, \(\sigma\) is the \(3\times 3\) matrix of electric conductivities, \(\tilde E\) a given vector function. An existence theorem for the solution is proved, and an error estimation for a finite element approximation of the 3D problem is presented. Some particular results for the 2D problem are obtained. Two numerical experiments are presented.
Reviewer: I.Grosu

MSC:
65Z05 Applications to the sciences
65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
78A25 Electromagnetic theory (general)
35Q99 Partial differential equations of mathematical physics and other areas of application
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